{
  "abstract": "The Boros-Moll sequences $\\{d_i(m)\\}_{0\\leq i\\leq m}$ are defined as $$d_i(m)=2^{-2m}\\sum_{k=i}^m 2^k \\binom{2m-2k}{m-k}\\binom{m+k}{k}\\binom{k}{i}.$$ Consider the ratio sequence $$u_i(m)=\\frac{d_{i-1}(m)d_{i+1}(m)}{d_i(m)^2}.$$ Chen and Gu conjectured that $\\{u_i(m)\\}_{2\\leq i \\leq m-2}$ is both reverse ultra log-concave and log-concave. In this paper, we prove the reverse ultra log-concavity conjecture using bounds of Chen-Gu and Zhao, and prove the log-concavity conjecture asymptotically by showing that $\\{u_i(m)\\}_{2\\leq i \\leq m-2}$ is strictly log-concave for all sufficiently large $m$. The key ingredient in the latter result is a recurrence of Kauers and Paule, which we interpret as a nonlinear discrete dynamical system through a backward map. We construct an approximation to the ratio sequence using its stable limiting fixed point and combine localization and contraction arguments with finite-difference estimates and separate interior and edge analyses to obtain the desired strict log-concavity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10234",
  "author_total": 1,
  "authors": [
    {
      "name": "Heshan Aravinda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c55178z76znd9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10234",
  "fulltext_url": null,
  "id": "c55178z76znd9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10234",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212162514",
  "pdf_url": "https://arxiv.org/pdf/2609.10234",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c55178z76znd9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.10234",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10234"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Two Conjectures Related to the Boros-Moll Sequences",
  "title_text": "On Two Conjectures Related to the Boros-Moll Sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/c55178z76znd9",
  "venue": "arXiv",
  "versions": []
}